Answer:
Explanation:
As the disc is unrolling from the thread then at any moment of the time
We have force equation as
also by torque equation we can say
Now we have
Also from above equation the tension force in the string is
The headlights are shining on a truck travelling at 100 km/h. The speed of the light from the headlights relative to the road wi
2 answers:
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(a) 18.9 m/s
The motion of the stone consists of two independent motions:
- A horizontal motion at constant speed
- A vertical motion with constant acceleration () downward
We can calculate the components of the initial velocity of the stone as it is launched from the ground:
The horizontal velocity remains constant, while the vertical velocity changes due to the acceleration along the vertical direction.
When the stone reaches the top of its parabolic path, the vertical velocity has became zero (because it is changing direction): so the speed of the stone is simply equal to the horizontal velocity, therefore
(b) 22.2 m/s
We can solve this part by analyzing the vertical motion only first. In fact, the vertical velocity at any height h during the motion is given by
(1)
where
is the initial vertical velocity
is the vertical velocity at height h
is the acceleration due to gravity (negative because it is downward)
At the top of the parabolic path, , so we can use the equation to find the maximum height
So, at half of the maximum height,
And so we can use again eq(1) to find the vertical velocity at h = 6.9 m:
And so, the speed of the stone at half of the maximum height is
(c) 17.4% faster
We said that the speed at the top of the trajectory (part a) is
while the speed at half of the maximum height (part b) is
So the difference is
And so, in percentage,
So, the stone in part (b) is moving 17.4% faster than in part (a).
The question is missing, but I guess the problem is asking for the distance between the cliff and the source of the sound.
First of all, we need to calculate the speed of sound at temperature of
:
The sound wave travels from the original point to the cliff and then back again to the original point in a total time of t=4.60 s. If we call L the distance between the source of the sound wave and the cliff, we can write (since the wave moves by uniform motion):
where v is the speed of the wave, 2L is the total distance covered by the wave and t is the time. Re-arranging the formula, we can calculate L, the distance between the source of the sound and the cliff:
First of all, we need to calculate the speed of sound at temperature of
The sound wave travels from the original point to the cliff and then back again to the original point in a total time of t=4.60 s. If we call L the distance between the source of the sound wave and the cliff, we can write (since the wave moves by uniform motion):
where v is the speed of the wave, 2L is the total distance covered by the wave and t is the time. Re-arranging the formula, we can calculate L, the distance between the source of the sound and the cliff: